Question: Tiffany is 2 times as old as Vanessa. 21 years ago, Tiffany was 9 times as old as Vanessa. How old is Tiffany now?
Solution: We can use the given information to write down two equations that describe the ages of Tiffany and Vanessa. Let Tiffany's current age be $t$ and Vanessa's current age be $v$ The information in the first sentence can be expressed in the following equation: $t = 2v$ 21 years ago, Tiffany was $t - 21$ years old, and Vanessa was $v - 21$ years old. The information in the second sentence can be expressed in the following equation: $t - 21 = 9(v - 21)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $t$ , it might be easiest to solve our first equation for $v$ and substitute it into our second equation. Solving our first equation for $v$ , we get: $v = t / 2$ . Substituting this into our second equation, we get: $t - 21 = 9($ $(t / 2)$ $- 21)$ which combines the information about $t$ from both of our original equations. Simplifying the right side of this equation, we get: $t - 21 = \dfrac{9}{2} t - 189$ Solving for $t$ , we get: $\dfrac{7}{2} t = 168$ $t = \dfrac{2}{7} \cdot 168 = 48$.